Question: The grades on a math midterm at Almond are normally distributed with $\mu = 83$ and $\sigma = 5.5$. Luis earned a n $84$ on the exam. Find the z-score for Luis's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Luis's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{84 - {83}}{{5.5}}} $ ${ z \approx 0.18}$ The z-score is $0.18$. In other words, Luis's score was $0.18$ standard deviations above the mean.